"The merciless criminal Kain has escaped from sub-space where he had been captured! Kain, who was deprived of his fredom by the Jurai royal family and GP (Galaxy Police), demolished the GP headquarters and attacked the Jurai King...His next target is...Earth!
"Around the same time, on earth, Tenchi's house has suddenly disappeared. What's even worse is that Tenchi's body is disappearing, too...! Something must have happened to Achika, Tenchi's mother, in the past! So the gang must leave for a journey to the year 1970."
(The movie seems to take place in the Universe timeline due to the fact that Kiyone is in it. But it seems as if the characters are more from the OAV due to the way they act and what their motives seem to be. There is no way of knowing for sure because there is no way of telling how the girls came across Tenchi. It's most definitely not from Tench in Tokyo though.)